Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the resetting position are Gaussian distributed with width σ . We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period and rate for different values of the ratio b =L /σ and find an interesting phase transition at a critical value b =bc . For bc<b <∞ , there is a metastable optimum time which disappears for b <bc . The intrinsic difficulties in implementing these protocols in experiments are also discussed.